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Symmetry group

3:56

Symmetry Groups of Triangles (Abstract Algebra)

1:24

Symmetries of a Tetrahedron

0:25

Guessing the Symmetry Group

1:51

Symmetry Group Theory Irreducible representation

0:25

Guessing the Symmetry Group

In group theory, the symmetry group of an object is the group of all transformations under which the object is invariant with composition as the group operation. For a space with a metric, it is a subgroup of the isometry group of the space concerned. If not stated otherwise, this article considers symmetry groups in Euclidean geometry, but the concept may also be studied in more general contexts as expanded below.
    • Introduction 

    • Two dimensions 

    • Three dimensions 

    • Symmetry groups in general 

    • Group structure in terms of symmetries